They may no longer be caching those pages, but there’s still something happening that’s not allowing the session to maintain state. We’ve seen this before where the server has object caching or similar and the garbage collection was clearing the session transients.
Can you contact your host and ask them if there’s a way they can allow the session to maintain state from one request to the next?
In a nutshell, what’s happening there is you select the ticket quantity, then click the Register Now button it correctly redirects to the registration checkout page, but the session data is not longer present so it shows the error. Minor technical point: The session data itself doesn’t contain the ticket selections, it acts like a key so the registration page can look up that information. It can’t look up that information if there is no key.